Synthesis and design of generalized chebyshev wideband hybrid ring based bandpass filters with a controllable transmission zero pair

A systematic and analytical method for the exact synthesis of generalized Chebyshev wideband hybrid ring based bandpass filters with a controllable transmission zero pair is developed in this paper. The basic configuration of the proposed filters consists of a hybrid ring, a multi-section short-circuited stub and a multi-section open-circuit stub. In this configuration, the position of the controllable transmission zero pair can be easily designed by setting the impedances of the multi-section short-circuited stub and the multi-section open-circuit stub. According to the position of the controllable transmission zero pair, two kinds of filters are proposed. The filter has a controllable transmission zero pair on the real axis (imaginary frequency) that they can be arranged to improve the group delay flatness. On the other hand, the filter has a controllable transmission zero pair on the imaginary axis (real frequency) and the desired stopband suppression can be obtained by adjusting the optimal position of them. This synthesis method is developed to obtain the impedance value of each line section and ripple factors of the filters with respect to given specifications (center frequency, passband bandwidth and transmission zeros). Two design examples, the fifth-order filter with a controllable imaginary frequency transmission zero pair and the fifth-order filter with a controllable real frequency transmission zero pair, are synthesized and fabricated. The measured results validate and confirm the theoretical predictions.